Some Results on (σ,τ) – Lie Ideals in Prime rings

Let R be a prime with characteristic not equal two, σ,τ : R →R be two automorphisms of R. and d be a nonzero derivation of R commuting with σ,τ .It is proved that : 1) Assume U ba a(σ,τ)-left Lie ideal of R. (a) If [U,U]σ,τ subset Cσ,τ and [U,U]=(0) ,then U subsetZ(R). (b) If [U,U]σ,τ subset Cσ,τ , then Usubset Z(R) . (c) If σ(v)+τ(v)notin Z(R) , for some vinU ,then there exists a nonzero left ideal A of R and a nonzero right ideal B of R such that [R,A]σ,τ inU , [R,B]σ,τsubsetU but [R,A]σ,τ nsubset Cσ,τ and [R,B]nsubset Cσ,τ . (d) If ad (u)=(0) (or d(u)a=(0)) for a in R , then a=0 or σ(u)+τ (u)notinZ(R) , for all u inU. 2) If U be a(σ,τ)-Lie ideal of R for a inR، d(u)a subset C σ,τ (or ad (u) in C σ,τ ),a in Z (R) , then a=0 or U subset Z (R). Also, in this paper we study some results when characteristic of R equal two and we show that the condition characteristic of R not equal two can not be excluded.